THE REPEATED MEDIAN INTERCEPT ESTIMATOR - INFLUENCE FUNCTION AND ASYMPTOTIC NORMALITY

Given the simple linear regression model Y-i = alpha + beta X(i) + e(i) for i = 1, ..., n, we consider the repeated median estimator of the intercept alpha, defined as ($) over cap alpha(n) = med(i) med(j,j not equal i) (X(j) Y-i - X(i) Y-j)/(X(j) - X(i)). We determine the influence function and prove asymptotic normality for ($) over cap alpha(n) when the carriers X(i) and error terms e(i) are random. The resulting influence function is bounded, and is the same as if the intercept is estimated by the median of the residuals from a preliminary slope estimator. With bivariate gaussian data the efficiency becomes 2/pi approximate to 63.7%. The asymptotic results are compared with sensitivity functions and finite-sample efficiencies. (C) 1995 Academic Press, Inc.